Let T be a linear transformation from a vector space V with dimension 11 onto a vector space W with dimension 7. What is the dimension of the nullspace of T?

The dimension of the nullspace of T = 4

Explanation:

The rank/dimension theorem is explains that:

Suppose V and W are vector spaces over F, and T:V → W is linear. If V is finite dimensional, then

nullity (T) + rank (T) = dim (V).

rank (T) = dimension of T = dim (T) = dim (W) = 7

nullity (T) = dimension of the nullspace of T = dim (T) = ?

dim (V) = 11

nullity (T) = dim (V) - dim (T) = 11 - 7

nullity (T) = 4.